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March 2019 Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups
Shinji Ohno, Takashi Sakai, Hajime Urakawa
Hiroshima Math. J. 49(1): 47-115 (March 2019). DOI: 10.32917/hmj/1554516038

Abstract

We give a necessary and su‰cient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By this criterion, we determine all the proper biharmonic orbits of these Lie group actions under some additional settings. As a consequence, we obtain many examples of proper biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups.

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Shinji Ohno. Takashi Sakai. Hajime Urakawa. "Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups." Hiroshima Math. J. 49 (1) 47 - 115, March 2019. https://doi.org/10.32917/hmj/1554516038

Information

Received: 4 August 2017; Revised: 27 May 2018; Published: March 2019
First available in Project Euclid: 6 April 2019

zbMATH: 07090064
MathSciNet: MR3936648
Digital Object Identifier: 10.32917/hmj/1554516038

Subjects:
Primary: 58E20
Secondary: 53C43

Rights: Copyright © 2019 Hiroshima University, Mathematics Program

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Vol.49 • No. 1 • March 2019
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